package ‘ca’ - the comprehensive r archive network · pdf filepackage...

Package ‘ca’December 14, 2016

Version 0.70

Date 2016-12-11

Title Simple, Multiple and Joint Correspondence Analysis

Author Michael Greenacre [aut], Oleg Nenadic [aut, cre], Michael Friendly [ctb]

Maintainer Oleg Nenadic <[email protected]>

Depends R (>= 3.0.0)

Suggests rgl (>= 0.64-10), vcd

Description Computation and visualization of simple, multiple and joint correspondence analysis.

LazyLoad yes

LazyData yes

License GPL

URL http://www.carme-n.org/

Repository CRAN

Repository/R-Forge/Project ca0

Repository/R-Forge/Revision 38

Repository/R-Forge/DateTimeStamp 2016-12-13 19:53:20

Date/Publication 2016-12-14 12:19:51

NeedsCompilation no

R topics documented:author . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2ca . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2caconv . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5cacoord . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6iterate.mjca . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7mjca . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8multilines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11pchlist . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12plot.ca . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

1

http://www.carme-n.org/

2 ca

plot.mjca . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16plot3d.ca . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18print.ca . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20print.mjca . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21print.summary.ca . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22print.summary.mjca . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22smoke . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23summary.ca . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23summary.mjca . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24wg93 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

Index 26

author Author dataset

Description

This data matrix contains the counts of the 26 letters of the alphabet (columns of matrix) for 12different novels (rows of matrix). Each row contains letter counts in a sample of text from eachwork, excluding proper nouns.

Usage

data("author")

Format

Data frame containing the 12 x 26 matrix.

Source

Larsen, W.A. and McGill, R., unpublished data collected in 1973.

ca Simple correspondence analysis

Description

Computation of simple correspondence analysis.

ca 3

Usage

ca(obj, ...)

## S3 method for class 'matrix'ca(obj, nd = NA, suprow = NA, supcol = NA,

subsetrow = NA, subsetcol = NA, ...)

## S3 method for class 'data.frame'ca(obj, ...)

## S3 method for class 'table'ca(obj, ...)

## S3 method for class 'xtabs'ca(obj, ...)

## S3 method for class 'formula'ca(formula, data, ...)

Arguments

obj,formula The function is generic, accepting various forms of the principal argument forspecifying a two-way frequency table. Currently accepted forms are matrices,data frames (coerced to frequency tables), objects of class "xtabs" or "table"and one-sided formulae of the form ~ F1 + F2, where F1 and F2 are factors.

nd Number of dimensions to be included in the output; if NA the maximum possibledimensions are included.

suprow Indices of supplementary rows.

supcol Indices of supplementary columns.

subsetrow Row indices of subset.

subsetcol Column indices of subset.

data A data frame against which to preferentially resolve variables in the formula

... Other arguments passed to the ca.matrix method

Details

The function ca computes a simple correspondence analysis based on the singular value decompo-sition.The options suprow and supcol allow supplementary (passive) rows and columns to be specified.Using the options subsetrow and/or subsetcol result in a subset CA being performed.

Value

sv Singular values

nd Dimenson of the solution

4 ca

rownames Row namesrowmass Row massesrowdist Row chi-square distances to centroidrowinertia Row inertiasrowcoord Row standard coordinatesrowsup Indices of row supplementary pointscolnames Column namescolmass Column massescoldist Column chi-square distances to centroidcolinertia Column inertiascolcoord Column standard coordinatescolsup Indices of column supplementary pointsN The frequency table

References

Nenadic, O. and Greenacre, M. (2007). Correspondence analysis in R, with two- and three-dimensionalgraphics: The ca package. Journal of Statistical Software, 20 (3), http://www.jstatsoft.org/v20/i03/

Greenacre, M. (2007). Correspondence Analysis in Practice. Second Edition. London: Chapman& Hall / CRC. Blasius, J. and Greenacre, M. J. (1994), Computation of correspondence analysis, inCorrespondence Analysis in the Social Sciences, pp. 53-75, London: Academic Press.

Greenacre, M.J. and Pardo, R. (2006), Subset correspondence analysis: visualizing relationshipsamong a selected set of response categories from a questionnaire survey. Sociological Methods andResearch, 35, pp. 193-218.

See Also

svd, plot.ca, plot3d.ca, summary.ca, print.ca

Examples

data("author")ca(author)plot(ca(author))

# table methodhaireye <- margin.table(HairEyeColor, 1:2)haireye.ca <- ca(haireye)haireye.caplot(haireye.ca)# some plot optionsplot(haireye.ca, lines=TRUE)plot(haireye.ca, arrows=c(TRUE, FALSE))

http://www.jstatsoft.org/v20/i03/


caconv 5

caconv Converting data types in CA and MCA

Description

Conversion from and to a number of different data types commonly used in CA and MCA (fre-quency tables, response pattern matrices, indicator matrices and Burt matrices).

Usage

caconv(x, from = c("freq", "rpm", "ind", "Burt"), to = c("rpm", "ind", "Burt", "freq"),nlev = NA, vars = c(1,2), ...)

Arguments

x A matrix (two-way frequency table, indicator matrix, or Burt matrix) or dataframe (response pattern matrix).

from The type of input data in x: a frequency table ("freq"), or a response patternmatrix ("rpm"), or an indicator matrix ("ind"), or a Burt matrix ("Burt").

to The data type into which x should be converted.

nlev A vector containing the number of levels for each categorical variable (for from="ind"or from="Burt"). If NA, nlev is computed from the data.

vars A vector of length 2 specifying the index of the variables to use for convertingto "freq" (i.e. to a regular two-way frequency table).

... Further arguments (ignored).

Details

The function caconv converts between data types in CA and MCA. Note that a conversion fromfrom="Burt" to to="ind" or to="rpm" is not supported.

Value

A matrix or data frame containing the converted data (with the type specified in to).

See Also

ca,mjca

6 cacoord

cacoord Extracting coordinates from ca and mjca objects.

Description

Extracting standard and principal coordinates as well as various row and column scaling configura-tions for visual display from ca and mjca objects.

Usage

cacoord(obj,type = c("standard", "principal",

"symmetric", "rowprincipal", "colprincipal", "symbiplot","rowgab", "colgab", "rowgreen", "colgreen"),

dim = NA,rows = NA,cols = NA,...)

Arguments

obj A ca or mjca object returned by ca or mjca.

type The type of coordinates to extract ("standard" or "principal"). The remain-ing options ("symmetric", ..., "colgreen") return the corresponding row/columncoordinate configuration for the map scaling options described in plot.ca wherethe corresponding argument is map.

dim The dimensions to return. If NA, all available dimensions are returned.

rows Logical indicating whether to return the row coordinates (see below for details).

cols Logical indicating whether to return the column coordinates (see below for de-tails).

... Further arguments (ignored).

Details

The function cacoord returns the standard or principal coordinates of a CA or MCA solution. Addi-tionally, row and column scaling configurations for plotting methods can be computed (see plot.cafor details).Note that by default row and column coordinates are computed (i.e. for (rows=NA&cols=NA)|(rows=TRUE&cols=TRUE)).Using rows=TRUE (and cols=NA or cols=FALSE) returns a matrix with the row coordinates, and forcols=TRUE (and cols=NA or cols=FALSE) a matrix with the column coordinates is returned.

Value

A list with the slots rows (row coordinates) and columns (column coordinates). When computingonly row or only column coordinates, a matrix (with the corresponding row or column coordinates)is returned.

iterate.mjca 7

See Also

ca,mjca,plot.ca,plot.mjca

iterate.mjca Updating a Burt matrix in Joint Correspondence Analysis

Description

Updating a Burt matrix in Joint Correspondence Analysis based on iteratively weighted least squares.

Usage

iterate.mjca(B, lev.n, nd = 2, maxit = 50, epsilon = 0.0001)

Arguments

B A Burt matrix.

lev.n The number of levels for each factor from the original response pattern matrix.

nd The required dimensionality of the solution.

maxit The maximum number of iterations.

epsilon A convergence criterion for the maximum absolute difference of updated valuescompared to the previous values. The iteration is completed when all differencesare smaller than epsilon.

Details

The function iterate.mjca computes the updated Burt matrix. This function is called from thefunction mjca when the option lambda="JCA", i.e. when a Joint Correspondence Analysis is per-formed.

Value

B.star The updated Burt matrix

crit Vector of length 2 containing the number of iterations and epsilon

See Also

mjca

8 mjca

mjca Multiple and joint correspondence analysis

Description

Computation of multiple and joint correspondence analysis.

Usage

mjca(obj, ...)

## S3 method for class 'data.frame'mjca(obj, ...)## S3 method for class 'table'mjca(obj, ...)## S3 method for class 'array'mjca(obj, ...)

## Default S3 method:mjca(obj, nd = 2, lambda = c("adjusted", "indicator", "Burt", "JCA"),

supcol = NA, subsetcat = NA,ps = ":", maxit = 50, epsilon = 0.0001, reti = FALSE, ...)

Arguments

obj A response pattern matrix (data frame containing factors), or a frequency table(a “table” object) or an integer array.

nd Number of dimensions to be included in the output; if NA the maximum possibledimensions are included.

lambda Gives the scaling method. Possible values include "indicator", "Burt", "adjusted"and "JCA". Using lambda = "JCA" results in a joint correspondence analysisusing iterative adjusment of the Burt matrix in the solution space. See Detailsfor descriptions of these options.

supcol Indices of supplementary columns.

subsetcat Indices of subset categories (previously subsetcol).

ps Separator used for combining variable and category names.

maxit The maximum number of iterations (Joint Correspondence Analysis).

epsilon A convergence criterion (Joint Correspondence Analysis).

reti Logical indicating whether the indicator matrix should be included in the output.

... Arguments passed to mjca.default

mjca 9

Details

The function mjca computes a multiple or joint correspondence analysis based on the eigenvalue de-composition of the Burt matrix. The lambda option selects the scaling variant desired for reportinginertias.

• lambda="indicator" gives multiple correspondence analysis based on the correspondenceanalysis of the indicator matrix, with corresponding inertias (eigenvalues).

• lambda="Burt" gives the version of multiple correspondence analysis based on the corre-spondence analysis of the Burt matrix, the inertias of which are the squares of those for theindicator option.

• lambda="adjusted" is the default option, giving improved percentages of inertia based onfitting the off-diagonal submatrices of the Burt matrix by rescaling the multiple correspon-dence analysis solution. All these first three options give the same standard coordinates of thecategories.

• lambda="JCA" gives a joint correspondence analysis, which uses an iterative algorithm thatoptimally fits the off-diagonal submatrices of the Burt matrix. The JCA solution does nothave strictly nested dimensions, so the percentage of inertia explained is given for the wholesolution of chosen dimensionality, not for each dimension, but this percentage is optimal.

Value

sv Eigenvalues (lambda = "indicator") or singular values (lambda = "Burt","adjusted" or "JCA")

lambda Scaling method

inertia.e Percentages of explained inertia

inertia.t Total inertia

inertia.et Total percentage of explained inertia with the nd-dimensional solution

levelnames Names of the factor/level combinations, joined using ps

factors A matrix containing the names of the factors and the names of the factor levels

levels.n Number of levels in each factor

nd User-specified dimensionality of the solution

nd.max Maximum possible dimensionality of the solution

rownames Row names

rowmass Row masses

rowdist Row chi-square distances to centroid

rowinertia Row inertias

rowcoord Row standard coordinates

rowpcoord Row principal coordinates

rowctr Row contributions

rowcor Row squared correlations

colnames Column names

colmass Column masses

10 mjca

coldist Column chi-square distances to centroid

colinertia Column inertias

colcoord Column standard coordinates

colpcoord Column principal coordinates

colctr column contributions

colcor Column squared correlations

colsup Indices of column supplementary points (of the Burt and Indicator matrix)

subsetcol Indices of subset columns (subsetcat)

Burt Burt matrix

Burt.upd The updated Burt matrix (JCA only)

subinertia Inertias of sub-matrices

JCA.iter Vector of length two containing the number of iterations and the epsilon (JCAonly)

indmat Indicator matrix if reti was set to TRUE

call Return of match.call

References

Nenadic, O. and Greenacre, M. (2007), Correspondence analysis in R, with two- and three-dimensionalgraphics: The ca package. Journal of Statistical Software, 20 (3), http://www.jstatsoft.org/v20/i03/Nenadic, O. and Greenacre, M. (2007), Computation of Multiple Correspondence Analysis, withCode in R, in Multiple Correspondence Analysis and Related Methods (eds. M. Greenacre and J.Blasius), Boca Raton: Chapmann & Hall / CRC, pp. 523-551.Greenacre, M.J. and Pardo, R. (2006), Subset correspondence analysis: visualizing relationshipsamong a selected set of response categories from a questionnaire survey. Sociological Methods andResearch, 35, pp. 193-218.

See Also

eigen, plot.mjca, summary.mjca, print.mjca

Examples

data("wg93")mjca(wg93[,1:4])

# table inputdata(UCBAdmissions)mjca(UCBAdmissions)## Not run: plot(mjca(UCBAdmissions))

### Different approaches to multiple correspondence analysis:# Multiple correspondence analysis based on the indicator matrix:## Not run: mjca(wg93[,1:4], lambda = "indicator")



multilines 11

# Multiple correspondence analysis based on the Burt matrix:## Not run: mjca(wg93[,1:4], lambda = "Burt")

# "Adjusted" multiple correspondence analysis (default setting):## Not run: mjca(wg93[,1:4], lambda = "adjusted")

# Joint correspondence analysis:## Not run: mjca(wg93[,1:4], lambda = "JCA")

### Subset analysis and supplementary variables:# Subset analysis:## Not run: mjca(wg93[,1:4], subsetcat = (1:20)[-seq(3,18,5)])

# Supplementary variables:## Not run: mjca(wg93, supcol = 5:7)

multilines Draw lines for groups distinguished by a factor

Description

This is a convenience function for drawing a set of lines distinguished by the levels of a factor. Itcan be used to make more attractive plots than available via plot.mjca.

Usage

multilines(XY, group=NULL, which=1:nf, sort=1, type='l', col=palette(), lwd=1, ...)

Arguments

XY A two-column data frame or matrix

group A factor; a separate line is drawn for each level included in which

which An integer vector used to select the factors for which lines are drawn. By default,all lines are drawn.

sort Column of XY to sort upon before drawing the line for each group

type Line type: "l" for line, "b" for line and points

col A vector of colors to be used for the various lines, in the order of the levels ingroup; recycled as necessary.

lwd A vector of line widths to be used for the various lines; recycled as necessary

... Other graphic parameters passed to lines, e.g., lty

Value

none

12 pchlist

Author(s)

Michael Friendly

See Also

lines

Examples

if (require(vcd)) {data(PreSex, package="vcd")presex.mca <- mjca(PreSex)res <- plot(presex.mca, labels=0, pch='.', cex.lab=1.2)coords <- data.frame(res$cols, presex.mca$factors)nlev <- rle(as.character(coords$factor))$lengthsfact <- unique(as.character(coords$factor))

cols <- c("blue", "red", "brown", "black")lwd <- c(2, 2, 2, 4)

plot(Dim2 ~ Dim1, type='n', data=coords)points(coords[,1:2], pch=rep(16:19, nlev), col=rep(cols, nlev), cex=1.2)text(coords[,1:2], labels=coords$level, col=rep(cols, nlev), pos=3, cex=1.2, xpd=TRUE)

multilines(coords[, c("Dim1", "Dim2")], group=coords$factor, col=cols, lwd=lwd)}

pchlist Listing the set of available symbols.

Description

A plot of the available symbols for use with the option pch.

Usage

pchlist()

Details

This function generates a numbered list of the plotting symbols available for use in the functionsplot.ca and plot3d.ca.

See Also

plot.ca, plot3d.ca

plot.ca 13

Examples

pchlist()

plot.ca Plotting 2D maps in correspondence analysis

Description

Graphical display of correspondence analysis results in two dimensions

Usage

## S3 method for class 'ca'plot(x, dim = c(1,2), map = "symmetric", what = c("all", "all"),

mass = c(FALSE, FALSE), contrib = c("none", "none"),col = c("blue", "red"),pch = c(16, 21, 17, 24),labels = c(2, 2),arrows = c(FALSE, FALSE),lines = c(FALSE, FALSE),lwd=1,xlab = "_auto_", ylab = "_auto_",col.lab = c("blue", "red"), ...)

Arguments

x Simple correspondence analysis object returned by ca

dim Numerical vector of length 2 indicating the dimensions to plot on horizontaland vertical axes respectively; default is first dimension horizontal and seconddimension vertical.

map Character string specifying the map type. Allowed options include"symmetric" (default)"rowprincipal""colprincipal""symbiplot""rowgab""colgab""rowgreen""colgreen"

what Vector of two character strings specifying the contents of the plot. First entrysets the rows and the second entry the columns. Allowed values are"all" (all available points, default)"active" (only active points are displayed)"passive" (only supplementary points are displayed)"none" (no points are displayed)The status (active or supplementary) of rows and columns is set in ca using theoptions suprow and supcol.

14 plot.ca

mass Vector of two logicals specifying if the mass should be represented by the areaof the point symbols (first entry for rows, second one for columns)

contrib Vector of two character strings specifying if contributions (relative or absolute)should be represented by different colour intensities. Available options are"none" (contributions are not indicated in the plot)."absolute" (absolute contributions are indicated by colour intensities)."relative" (relative contributions are indicated by colour intensities).If set to "absolute" or "relative", points with zero contribution are displayedin white. The higher the contribution of a point, the closer the correspondingcolour to the one specified by the col option.

col Vector of length 2 specifying the colours of row and column point symbols, bydefault blue for rows and red for columns. Colours can be entered in hexadeci-mal (e.g. "#FF0000"), rgb (e.g. rgb(1,0,0)) values or by R-name (e.g. "red").

pch Vector of length 4 giving the type of points to be used for row active and sup-plementary, column active and supplementary points. See pchlist for a list ofsymbols.

labels Vector of length two specifying if the plot should contain symbols only (0),labels only (1) or both symbols and labels (2). Setting labels to 2 results in thesymbols being plotted at the coordinates and the labels with an offset.

arrows Vector of two logicals specifying if the plot should contain points (FALSE, de-fault) or arrows (TRUE). First value sets the rows and the second value sets thecolumns.

lines Vector of two logicals specifying if the plot should join the points with lines(FALSE, default) or arrows (TRUE). First value sets the rows and the second valuesets the columns.

lwd Line width for arrows and lines

xlab, ylab Labels for horizontal and vertical axes. The default, "_auto_" means that thefunction auto-generates a label of the form Dimension X (xx.xx %

col.lab Vector of length 2 specifying the colours of row and column point labels

... Further arguments passed to plot and points.

Details

The function plot.ca makes a two-dimensional map of the object created by ca with respect to twoselected dimensions. By default the scaling option of the map is "symmetric", that is the so-calledsymmetric map. In this map both the row and column points are scaled to have inertias (weightedvariances) equal to the principal inertia (eigenvalue or squared singular value) along the principalaxes, that is both rows and columns are in pricipal coordinates. Other options are as follows:

• -"rowprincipal" or "colprincipal" - these are the so-called asymmetric maps, with eitherrows in principal coordinates and columns in standard coordinates, or vice versa (also knownas row-metric-preserving or column-metric-preserving respectively). These maps are biplots;

• -"symbiplot" - this scales both rows and columns to have variances equal to the singularvalues (square roots of eigenvalues), which gives a symmetric biplot but does not preserverow or column metrics;

plot.ca 15

• -"rowgab" or "colgab" - these are asymmetric maps (see above) with rows (respectively,columns) in principal coordinates and columns (respectively, rows) in standard coordinatesmultiplied by the mass of the corresponding point. These are also biplots and were proposedby Gabriel & Odoroff (1990);

• -"rowgreen" or "colgreen" - these are similar to "rowgab" and "colgab" except that thepoints in standard coordinates are multiplied by the square root of the corresponding masses,giving reconstructions of the standardized residuals.

This function has options for sizing and shading the points. If the option mass is TRUE for a set ofpoints, the size of the point symbol is proportional to the relative frequency (mass) of each point.If the option contrib is "absolute" or "relative" for a set of points, the colour intensity ofthe point symbol is proportional to the absolute contribution of the points to the planar display or,respectively, the quality of representation of the points in the display. To globally resize all thepoints (and text labels), use par("cex"=) before the plot.

Value

In addition to the side effect of producing the plot, the function invisibly returns the coordinatesof the plotted points, a list of two components, with names rows and cols. These can be used tofurther annotate the plot using base R plotting functions.

References

Gabriel, K.R. and Odoroff, C. (1990). Biplots in biomedical research. Statistics in Medicine, 9, pp.469-485.Greenacre, M.J. (1993) Correspondence Analysis in Practice. London: Academic Press.Greenacre, M.J. (1993) Biplots in correspondence Analysis, Journal of Applied Statistics, 20, pp.251 - 269.

See Also

ca, summary.ca, print.ca, plot3d.ca, pchlist

Examples

data("smoke")

# A two-dimensional map with standard settingsplot(ca(smoke))

# Mass for rows and columns represented by the size of the point symbolsplot(ca(smoke), mass = c(TRUE, TRUE))

# Displaying the column profiles only with masses represented by size of point# symbols and relative contributions by colour intensity.# Since the arguments are recycled it is sufficient to give only one argument# for mass and contrib.data("author")plot(ca(author), what = c("none", "all"), mass = TRUE, contrib = "relative")

16 plot.mjca

plot.mjca Plotting 2D maps in multiple and joint correspondence analysis

Description

Graphical display of multiple and joint correspondence analysis results in two dimensions

Usage

## S3 method for class 'mjca'plot(x, dim = c(1,2), map = "symmetric", centroids = FALSE,

what = c("none", "all"), mass = c(FALSE, FALSE),contrib = c("none", "none"), col = c("#000000", "#FF0000"),pch = c(16, 1, 17, 24),labels = c(2, 2), collabels = c("both", "level", "factor"),arrows = c(FALSE, FALSE), xlab = "_auto_", ylab = "_auto_", ...)

Arguments

x Multiple or joint correspondence analysis object returned by mjca

dim Numerical vector of length 2 indicating the dimensions to plot on horizontaland vertical axes respectively; default is first dimension horizontal and seconddimension vertical.


centroids Logical indicating if column centroids should be added to the plot

what Vector of two character strings specifying the contents of the plot. First entrysets the rows and the second entry the columns. Allowed values are"all" (all available points, default)"active" (only active points are displayed)"passive" (only supplementary points are displayed)"none" (no points are displayed)The status (active or supplementary) of columns is set in mjca using the optionsupcol.

mass Vector of two logicals specifying if the mass should be represented by the areaof the point symbols (first entry for rows, second one for columns)

plot.mjca 17

contrib Vector of two character strings specifying if contributions (relative or absolute)should be represented by different colour intensities. Available options are"none" (contributions are not indicated in the plot)."absolute" (absolute contributions are indicated by colour intensities)."relative" (relative contributions are indicated by colour intensities).If set to "absolute" or "relative", points with zero contribution are displayedin white. The higher the contribution of a point, the closer the correspondingcolour to the one specified by the col option.

col Vector of length 2 specifying the colours of row and column point symbols, bydefault black for rows and red for columns. Colours can be entered in hexadeci-mal (e.g. "#FF0000"), rgb (e.g. rgb(1,0,0)) values or by R-name (e.g. "red").

pch Vector of length 4 giving the type of points to be used for row active and sup-plementary, column active and supplementary points. See pchlist for a list ofsymbols.


collabels Determines the format used for column labels, when the columns are labeled inthe plot."both" uses the factor names and level value, in the form "factor:level""level" uses the factor level value only"factor" uses the factor name only


xlab, ylab Labels for horizontal and vertical axes. The default, "_auto_" means that thefunction auto-generates a label of the form Dimension X (xx.xx %)

... Further arguments passed to plot and points.

Details

The function plot.mjca makes a two-dimensional map of the object created by mjca with respectto two selected dimensions. By default the scaling option of the map is "symmetric", that is theso-called symmetric map. In this map both the row and column points are scaled to have inertias(weighted variances) equal to the principal inertia (eigenvalue) along the principal axes, that is bothrows and columns are in pricipal coordinates. Other options are as follows:

• -"rowprincipal" or "colprincipal" - these are the so-called asymmetric maps, with eitherrows in principal coordinates and columns in standard coordinates, or vice versa (also knownas row-metric-preserving or column-metric-preserving respectively). These maps are biplots;

• -"symbiplot" - this scales both rows and columns to have variances equal to the singularvalues (square roots of eigenvalues), which gives a symmetric biplot but does not preserverow or column metrics;

• -"rowgab" or "colgab" - these are asymmetric maps (see above) with rows (respectively,columns) in principal coordinates and columns (respectively, rows) in standard coordinates

18 plot3d.ca

multiplied by the mass of the corresponding point. These are also biplots and were proposedby Gabriel & Odoroff (1990);

• -"rowgreen" or "colgreen" - these are similar to "rowgab" and "colgab" except that thepoints in standard coordinates are multiplied by the square root of the corresponding masses,giving reconstructions of the standardized residuals.

This function has options for sizing and shading the points. If the option mass is TRUE for a set ofpoints, the size of the point symbol is proportional to the relative frequency (mass) of each point.If the option contrib is "absolute" or "relative" for a set of points, the colour intensity ofthe point symbol is proportional to the absolute contribution of the points to the planar display or,respectively, the quality of representation of the points in the display. To globally resize all thepoints (and text labels), use par("cex"=) before the plot.

Value

In addition to the side effect of producing the plot, the function invisibly returns the coordinatesof the plotted points, a list of two components, with names rows and cols. These can be used tofurther annotate the plot using base R plotting functions.

References

Gabriel, K.R. and Odoroff, C. (1990). Biplots in biomedical research. Statistics in Medicine, 9, pp.469-485.Greenacre, M.J. (1993) Correspondence Analysis in Practice. London: Academic Press.Greenacre, M.J. (1993) Biplots in correspondence Analysis, Journal of Applied Statistics, 20, pp.251 - 269.

See Also

mjca, summary.mjca, print.mjca, pchlist

Examples

data("wg93")

# A two-dimensional map with standard settingsplot(mjca(wg93[,1:4]))

plot3d.ca Plotting 3D maps in correspondence analysis

Description

Graphical display of correspondence analysis in three dimensions

plot3d.ca 19

Usage

## S3 method for class 'ca'plot3d(x, dim = c(1, 2, 3), map = "symmetric", what = c("all", "all"),

contrib = c("none", "none"), col = c("#6666FF","#FF6666"),labcol = c("#0000FF", "#FF0000"), pch = c(16, 1, 18, 9),labels = c(2, 2), sf = 0.00001, arrows = c(FALSE, FALSE),axiscol = "#333333", axislcol = "#333333",

laboffset = list(x = 0, y = 0.075, z = 0.05), ...)

Arguments


dim Numerical vector of length 2 indicating the dimensions to plot


what Vector of two character strings specifying the contents of the plot. First entrysets the rows and the second entry the columns. Allowed values are"none" (no points are displayed)"active" (only active points are displayed, default)"supplementary" (only supplementary points are displayed)"all" (all available points)The status (active or supplementary) is set in ca.

contrib Vector of two character strings specifying if contributions (relative or absolute)should be indicated by different colour intensities. Available options are"none" (contributions are not indicated in the plot)."absolute" (absolute contributions are indicated by colour intensities)."relative" (relative conrributions are indicated by colour intensities).If set to "absolute" or "relative", points with zero contribution are displayedin white. The higher the contribution of a point, the closer the correspondingcolour to the one specified by the col option.

col Vector of length 2 specifying the colours of row and column profiles. Colourscan be entered in hexadecimal (e.g. "#FF0000"), rgb (e.g. rgb(1,0,0)) valuesor by R-name (e.g. "red").

labcol Vector of length 2 specifying the colours of row and column labels.

pch Vector of length 2 giving the type of points to be used for rows and columns.


sf A scaling factor for the volume of the 3d primitives.

20 print.ca


axiscol Colour of the axis line.

axislcol Colour of the axis labels.

laboffset List with 3 slots specifying the label offset in x, y, and z direction.

... Further arguments passed to the rgl functions.

See Also

ca

print.ca Printing ca objects

Description

Printing method for correspondence analysis objects

Usage

## S3 method for class 'ca'print(x, ...)

Arguments


... Further arguments are ignored

Details

The function print.ca gives the basic statistics of the ca object. First the eigenvalues (that is, prin-cipal inertias) and their percentages with respect to total inertia are printed. Then for the rows andcolumns respectively, the following are printed: the masses, chi-square distances of the points to thecentroid (i.e., centroid of the active points), point inertias (for active points only) and principal co-ordinates on the first nd dimensions requested (default = 2 dimensions). The function summary.cagives more detailed results about the inertia contributions of each point on each principal axis.For supplementary points, masses and inertias are not applicable.

See Also

ca

Examples

data("smoke")print(ca(smoke))

print.mjca 21

print.mjca Printing mjca objects

Description

Printing method for multiple and joint correspondence analysis objects

Usage

## S3 method for class 'mjca'print(x, ...)

Arguments

x Multiple or joint correspondence analysis object returned by mjca


Details

The function print.mjca gives the basic statistics of the mjca object. First the eigenvalues (thatis, principal inertias) and their percentages with respect to total inertia are printed. Then for therows and columns respectively, the following are printed: the masses, chi-square distances of thepoints to the centroid (i.e., centroid of the active points), point inertias (for active points only) andprincipal coordinates on the first nd dimensions requested (default = 2 dimensions). The functionsummary.mjca gives more detailed results about the inertia contributions of each point on eachprincipal axis.For supplementary points, masses and inertias are not applicable.

See Also

mjca

Examples

data("wg93")print(mjca(wg93[,1:4]))# equivalent to:mjca(wg93[,1:4])

22 print.summary.mjca

print.summary.ca Printing summeries of ca objects

Description

Printing method for summaries of correspondence analysis objects

Usage

## S3 method for class 'summary.ca'print(x, ...)

Arguments

x Summary of a simple correspondence analysis object returned by summary.ca


See Also

ca, summary.ca

print.summary.mjca Printing summeries of mjca objects

Description

Printing method for summaries of multiple and joint correspondence analysis objects

Usage

## S3 method for class 'summary.mjca'print(x, ...)

Arguments

x summary of a multiple or joint correspondence analysis object returned by summary.mjca


See Also

mjca, summary.mjca

smoke 23

smoke Smoke dataset

Description

Artificial dataset in Greenacre (1984)

Usage

data(smoke)

Format

Table containing 5 rows (staff group) and 4 columns (smoking categories), giving the frequenciesof smoking categories in each staff group in a fictional organization.

References

Greenacre, M.J. (1984). Theory and Applications of Correspondence Analysis. London: AcademicPress.

summary.ca Summarizing simple correspondence analysis

Description

Printed output summarizing the results of ca, including a scree-plot of the principal inertias and rowand column contributions.

Usage

## S3 method for class 'ca'summary(object, scree = TRUE, rows=TRUE, columns=TRUE, ...)

Arguments

object Simple correspondence analysis object returned by ca.

scree Logical flag specifying if a scree-plot should be included in the output.

rows Logical: should row contribution summaries be included?

columns Logical: should column contribution summaries be included?

... Further arguments (ignored)

24 summary.mjca

Details

The function summary.ca gives the detailed numerical results of the ca function. All the eigenvalues(principal inertias) are listed, their percentages with respect to total inertia, and a bar chart (alsoknown as a scree plot). Then for the set of rows and columns a table of results is given in a standardformat, where quantities are either multiplied by 1000 or expressed in permills (thousandths): themass of each point (x1000), the quality of display in the solution subspace of nd dimensions, theinertia of the point (in permills of the total inertia), and then for each dimension of the solutionthe principal coordinate (x1000), the (relative) contribution COR of the principal axis to the pointinertia (x1000) and the (absolute) contribution CTR of the point to the inertia of the axis (in permillsof the principal inertia).For supplementary points, masses, inertias and absolute contributions (CTR) are not applicable, butthe relative contributions (COR) are valid as well as their sum over the set of chosen nd dimensions(QLT).

Examples

data("smoke")summary(ca(smoke))

summary.mjca Summarizing multiple and joint correspondence analysis

Description

Textual output summarizing the results of mjca, including a scree-plot of the principal inertias androw and column contributions.

Usage

## S3 method for class 'mjca'summary(object, scree = TRUE, rows = FALSE, columns = TRUE, ...)

Arguments

object Multiple or joint correspondence analysis object returned by mjca.

scree Logical flag specifying if a scree-plot should be included in the output.

rows Logical specifying whether the results for the rows should be included in theoutput (default = FALSE).

columns Logical specifying whether the results for the columns should be included in theoutput (default = TRUE).

... Further arguments (ignored)

wg93 25

Details

The function summary.mjca gives the detailed numerical results of the mjca function. All theeigenvalues (principal inertias) are listed, their percentages with respect to total inertia, and a barchart (also known as a scree plot). Then for the set of rows and columns a table of results isgiven in a standard format, where quantities are either multiplied by 1000 or expressed in permills(thousandths): the mass of each point (x1000), the quality of display in the solution subspace of nddimensions, the inertia of the point (in permills of the total inertia), and then for each dimension ofthe solution the principal coordinate (x1000), the (relative) contribution COR of the principal axisto the point inertia (x1000) and the (absolute) contribution CTR of the point to the inertia of theaxis (in permills of the principal inertia).For supplementary points, masses, inertias and absolute contributions (CTR) are not applicable, butthe relative contributions (COR) are valid as well as their sum over the set of chosen nd dimensions(QLT).

Examples

data("wg93")summary(mjca(wg93[,1:4]))

wg93 International Social Survey Program on Environment 1993 - westernGerman sample

Description

This data frame contains records of four questions on attitude towards science with responses ona five-point scale (1=agree strongly to 5=disagree strongly) and three demographic variables (sex,age and education).

Usage

data(wg93)

Format

Data frame (871x7).

Source

ISSP (1993). International Social Survey Program: Environment. http://www.issp.org

http://www.issp.org

Index

∗Topic aplotmultilines, 11

∗Topic datasetsauthor, 2smoke, 23wg93, 25

∗Topic multivariateca, 2caconv, 5cacoord, 6iterate.mjca, 7mjca, 8

author, 2

ca, 2, 5–7, 13, 15, 19, 20, 22–24caconv, 5cacoord, 6

eigen, 10

iterate.mjca, 7

lines, 11, 12

mjca, 5–7, 8, 16, 18, 21, 22, 24, 25multilines, 11

pchlist, 12, 14, 15, 17, 18plot, 14, 17plot.ca, 4, 6, 7, 12, 13plot.mjca, 7, 10, 11, 16plot3d.ca, 4, 12, 15, 18points, 14, 17print.ca, 4, 15, 20print.mjca, 10, 18, 21print.summary.ca, 22print.summary.mjca, 22

smoke, 23summary.ca, 4, 15, 20, 22, 23

summary.mjca, 10, 18, 21, 22, 24svd, 4

wg93, 25

26

package ‘ca’ - the comprehensive r archive network · pdf filepackage...

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